I would rent the new 80-400 AF-S lens for the focusing speed it has, and the focal length range. The "old" 80-400 AF-D is a lens I have owned since it came out, and it is a slow, unreliable, erratic focuser much of the time. But from what I've read and seen from Thom Hogan, the new 80-400 AF-S is actually a VERY solid lens in optics, and in focusing, and he says it's very reliable for birds/nature, so, definitely it is a huge advance over the old, screw-driven focusing lens. I have a 70-300 VR-G...it's mostly okay, but it suffers from unreliable focusing; it misses, and FAILS to initiate focus quite often whenever distance changes are significant between the last focused distance and a new target at a different range; that is a well-known issue with the 70-300 VR,and has been mentioned here by me, and by two other TPFers, as well as being in the Hogan and Rockwell reviews...it's a well-known quirk/flaw/issue that the 70-300 VR-G suffers from. It doesn't always do this, but it does this often enough that you WILL miss shots because the damned lens will not initiate focus, and then the shot is...gone... It is after all, a consumer-grade lens, and it's built on value, not on ultimate performance or on ultimate optical quality.
The 300mm f/4 AF-S, the one that's been made for the last 15 years, is very sharp, light-ish in weight, not a speed-demon focusing, but it's no slouch either. However, fo a Nikon AF-S focusing lens, the 300/4 AF-S is NOT as fast as other AF-S lenses in terms of acquiring a new target--and it will, occasionally stutter. With the 1.4x converter added, the focusing gets very jittery and nervous.
The NEW, PF-E 300mm f/4 ($1,999) is exceptionally smaller than the older 300mm AF-S lens, is very light, and feels like a million bucks! I would LOVE the new 300 PF-E; the phase fresnel lens element design makes this about the same size as Canon's 135/2-L, or the Nikkor 24-70 AF-S G. I demo'd this lens a month ago, and damn--it is SWEET! Soooooooo compact for a 300!
If I were renting, I'd rent the 80-400 AF-S if I had to shoot from inside the oval.